Aiming at achieving the object grasping task, an inchworm-snake inspired flexible robotic manipulator (FRM) is presented in this article. By using both flexible and rigid materials in the robot structure, the FRM has the stability and control accuracy of a rigid robot as well as the compliant behavior of a soft robot. The piecewise-linear driving characteristic of the shape memory alloy (SMA) actuator enables the accurate establishment of the FRM's kinematic model and model-based control method. Deep learning-based eye-in-hand binocular visual perception is designed to obtain the state feedback without relying on external sensors, making it suitable to perform tasks in confined and unstructured environment. A model-based controller with the deformation planning is introduced with the aim of achieving accurate control in object grasping. The experiments demonstrate that the FRM possesses the capability of performing the object grasping with the proposed methods.